Poisson Process probabilities

Customers enter a shop according to a Poisson process of rate 1/2 per minute. Let C(t) be the number of customers who have entered the shop after it has been open for t minutes.

Suppose that each customer spends exactly 5 minutes in the shop. Find the distribution of the number of customers in the shop after it has been open for 1 hour.
d) What is the probability that the first and second customers to arrive do so within 1 minute of each other?